讨论了非线性脉冲双曲偏微分方程解的振动性质 ,利用微分不等式方法将所讨论的脉冲偏微分方程转化为脉冲时滞微分方程的问题 ,获得了其一切解不依赖状态脉冲的双曲Robin边值问题解振动的充分性判据 ;结论将脉冲微分方程的振动性质推广到具时滞的脉冲偏微分方程 ;同时也指出了脉冲和时滞在振动中的影响作用以及脉冲时滞偏微分方程解的振动性质在生物学、医学、工程学、化学、物理学等学科中的广泛应用。

Oscillation of Nonlinear Impulsive Hyperbolic Partial Differential Equations with Delay XUE Qiu-tiao 1,3 ,XU De-yi 2,LIU An-ping 1(1.Department of Mathematics and Physics, China University of Geosciences,Wuhan 430074, China;2. Faculty of Humanity and Economy, China University of Geosciences,Wuhan 430074, China;3.Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, China)In this paper, we study oscillatory properties of solutions to nonlinear impulsive hyperbolic partial differential equations with delay. It inverted the discussed impulsive delayed partial differential equations into impulsive delayed ordinary differential equations via the method of differential inequalities. Several sufficient criterias are established for oscillations of the solutions impulsive hyperbolic Robin boundary value problems. The results fully extend the oscillatory properties of impulsive differential equations to impulsive partial differential equations with delayed. It reflects the influence action of impulsive and delay in oscillations. The paper also showed that oscillatory properties of solutions to impulsive hyperbolic partial differential equations with delay have wide applications in such subjects as biology、medicine、engineering、chemistry and physics.hyperbolic equations; impulsive; oscillation